Download ACCRS/QUALITY CORE CORRELATION DOCUMENT: GEOMETRY

ACCRS/QUALITY CORE CORRELATION DOCUMENT:
GEOMETRY
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE
STANDARD
Experiment with transformations in the plane.
1. [G-CO1] Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of
point, line, distance along a line, and distance around a circular
arc.
2. [G-CO2] Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe transformations
as functions that take points in the plane as inputs and give other
points as outputs. Compare transformations that preserve distance
and angle to those that do not (e.g., translation versus horizontal
stretch).
3. [G-CO3] Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations and reflections that carry it onto
itself.
4. [G-CO4] Develop definitions of rotations, reflections, and translations
in terms of angles, circles, perpendicular lines, parallel lines, and
line segments.
5. [G-CO5] Given a geometric figure and a rotation, reflection, or
translation, draw the transformed figure using, e.g., graph paper,
tracing paper, or geometry software. Specify a sequence of
transformations that will carry a given figure onto another.
C.1.a Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use definitions, basic postulates, and theorems
about points, segments, lines, angles, and planes to write proofs
and to solve problems.
G.1.e Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Determine the effect of reflections,
rotations, translations, and dilations and their compositions on
the coordinate plane
C.1.a Using Logic and Proof to Reason Mathematically; 1. Logic
and Proof; Use definitions, basic postulates, and theorems
about points, segments, lines, angles, and planes to write proofs
and to solve problems.
E.1.e Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify and draw images of
transformations and use their properties to solve problems.
E.1.a Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Determine points or lines of
symmetry and apply the properties of symmetry to figures.
E.1.e Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify and draw images of
transformations and use their properties to solve problems.
Understand congruence in terms of rigid motion.
(Build on rigid motions as a familiar starting
point for development of concept of geometric
proof.)
6. [G-CO6] Use geometric descriptions of rigid motions to transform
figures and to predict the effect of a given rigid motion on a given
figure; given two figures, use the definition of congruence in terms
of rigid motions to decide if they are congruent.
7. [G-CO7] Use the definition of congruence in terms of rigid motions to
show that two triangles are congruent if and only if corresponding
pairs of sides and corresponding pairs of angles are congruent.
E.1.a Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Determine points or lines of
symmetry and apply the properties of symmetry to figures.
C.1.g Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use the principle that corresponding parts of
congruent triangles are congruent to solve problems. E.1.b Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify congruent figures and
their corresponding parts.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
8. [G-CO8] Explain how the criteria for triangle congruence (ASA, SAS,
and SSS) follow from the definition of congruence in terms of rigid
motions.
QUALITYCORE COURSE STANDARD
C.1.f Using Logic and Proof to Reason Mathematically; Logic
and Proof; Prove that two triangles are congruent by applying
the SSS, SAS, ASA, AAS, and HL congruence statements.
Prove geometric theorems. (Focus on validity of
underlying reasoning while using variety of
ways of writing proofs.)
9. [G-CO9] Prove theorems about lines and angles. Theorems include:
vertical angles are congruent; when a transversal crosses parallel
lines, alternate interior angles are congruent and corresponding
angles are congruent; points on a perpendicular bisector of a line
segment are exactly those equidistant from the segment’s
endpoints.
C.1.a Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use definitions, basic postulates, and theorems
about points, segments, lines, angles, and planes to write proofs
and to solve problems.
C.1.e Using Logic and Proof to Reason Mathematically; Logic
and Proof; Read and write different types and formats of
proofs including two-column, flowchart, paragraph, and indirect
proofs.
D.1.c Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Identify corresponding, same-side interior, same-side
exterior, alternate interior, and alternate exterior angle pairs
formed by a pair of parallel lines and a transversal and use
these special angle pairs to solve problems (e.g., solve
equations, use in proofs)
C.1.b Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use inductive reasoning to make conjectures and
deductive reasoning to arrive at valid conclusions.
D.1.b Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Identify vertical, adjacent, complementary, and
supplementary angle pairs and use them to solve problems
(e.g., solve equations, use in proofs)
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
10. [G-CO10] Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180 degrees;
base angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the third
side and half the length; the medians of a triangle meet at a
point.
QUALITYCORE COURSE STANDARD
C.1.e Using Logic and Proof to Reason Mathematically; Logic
and Proof; Read and write different types and formats of
proofs including two-column, flowchart, paragraph, and
indirect proofs. D.2.b Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Identify medians,
altitudes, perpendicular bisectors, and angle bisectors of
triangles and use their properties to solve problems.
D.2.j Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Apply the
Isosceles Triangle Theorem and its converse to triangles to
solve mathematical and real-world problems.
11. [G-CO11] Prove theorems about parallelograms. Theorems include:
opposite sides are congruent, opposite angles are congruent,
the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent
diagonals.
Make geometric constructions. (Formalize and
C.1.e Using Logic and Proof to Reason Mathematically; Logic
and Proof; Read and write different types and formats of
proofs including two-column, flowchart, paragraph, and
indirect proofs.
C.1.i Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use properties of special quadrilaterals in a proof.
D.2.g Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Identify and
classify quadrilaterals, including parallelograms, rectangles,
rhombi, squares, kites, trapezoids, and isosceles trapezoids,
using their properties.
explain processes.)
12. [G-CO12] Make formal geometric constructions with a variety of tools
and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.).
Constructions include copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line
segment; and constructing a line parallel to a given line through
a point not on the line.
D.1.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Identify and model plane figures, including collinear
and noncollinear points, lines, segments, rays, and angles
using appropriate mathematical symbols.
D.1.c Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Identify corresponding, same-side interior, same-side
exterior, alternate interior, and alternate exterior angle pairs
formed by a pair of parallel lines and a transversal and use
these special angle pairs to solve problems (e.g., solve
equations, use in proofs).
D.1.d Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Use construction techniques, including straightedge
and compass, to bisect and trisect segments and to create
parallel and perpendicular lines, perpendicular bisectors, and
angle bisectors.
13. [G-CO13] Construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
Understand similarity in terms of similarity
transformations.
14. [G-SRT1] Verify experimentally the properties of dilations given by a
center and a scale factor:
14a. [G-SRT1a] A dilation takes a line not passing through the center of
the dilation to a parallel line, and leaves a line passing through
the center unchanged.
14b. [G-SRT1b] The dilation of a line segment is longer or shorter in the
ratio given by the scale factor.
15. [G-SRT2] Given two figures, use the definition of similarity in terms
of similarity transformations to decide if they are similar; explain
using similarity transformations the meaning of similarity for
triangles as the equality of all corresponding pairs of angles and
the proportionality of all corresponding pairs of sides.
C.1.h Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use several methods, including AA, SAS, and
SSS, to prove that two triangles are similar, corresponding
sides are proportional, and corresponding angles are
congruent.
E.1.c Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify similar figures and
use ratios and proportions to solve mathematical and realworld problems (e.g., finding the height of a tree using the
shadow of the tree and the height and shadow of a person)
E.1.d Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Use the definition of similarity
to establish the congruence of angles, proportionality of
sides, and scale factor of two similar polygons.
16. [G-SRT3] Use the properties of similarity transformations to
establish the AA criterion for two triangles to be similar.
C.1.h Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use several methods, including AA, SAS, and SSS,
to prove that two triangles are similar, corresponding sides are
proportional, and corresponding angles are congruent.
Prove theorems involving similarity.
17. [G-SRT4] Prove theorems about triangles. Theorems include: a line
D.2.e Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Apply the
Pythagorean Theorem and its converse to triangles to solve
mathematical and real-world problems.
18. [G-SRT5] Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
D.2.d Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Solve problems
involving the relationships formed when the altitude to the
hypotenuse of a right triangle is drawn.
E.1.e Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify and draw images of
transformations and use their properties to solve problems.
parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
E.1.g. Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Determine the geometric mana
between two numbers and use it to solve problems (e.g., find the
lengths of segments in right triangles.)
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
Define trigonometric ratios and solve problems
involving right triangles.
19. [G-SRT6] Understand that by similarity, side ratios in right triangles
are properties of the angles in the triangle, leading to definitions
of trigonometric ratios for acute angles.
20. [G-SRT7] Explain and use the relationship between the sine and
cosine of complementary angles.
21. [G-SRT8] Use trigonometric ratios and the Pythagorean Theorem to
solve right triangles in applied problems.*
H.1.b Investigating and Applying Basic Ideas of Trigonometry;
Introduction to Trigonometry; Find the sine, cosine, and
tangent rations of acute angles given the side lengths of right
triangles.
H.1.b Investigating and Applying Basic Ideas of Trigonometry;
Introduction to Trigonometry; Find the sine, cosine, and
tangent rations of acute angles given the side lengths of right
triangles.
D.2.e Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Apply the
Pythagorean Theorem and its converse to triangles to solve
mathematical and real-world problems.
H.1.b Investigating and Applying Basic Ideas of Trigonometry;
Introduction to Trigonometry; Find the sine, cosine, and
tangent rations of acute angles given the side lengths of right
triangles.
H.1.c. Investigating and Applying Basic Ideas of Trigonometry;
Introduction to Trigonometry; Use trigonometric ratios to
find the sides or angles of right triangles and to solve realworld problems (e.g. use angles of elevation and depression to
find missing measures).
H.1.a Investigating and Applying Basic Ideas of Trigonometry;
Introduction to Trigonometry; Apply properties of 45-4590 and 30-60-90 triangle to determine lengths of right
triangles.
Apply trigonometry to general triangles.
22. [G-SRT9] Derive the formula A = (1/2)ab sin(C) for the area of a
triangle by drawing an auxiliary line from a vertex perpendicular
to the opposite side.
D.2.d Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Solve problems
involving the relationships formed when the altitude to the
hypotenuse of a right triangle is drawn.
D.2.f Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Identify and use
Pythagorean triples in right triangles to find lengths of the
unknown side.
F.2.a
23. [G-SRT10] Prove the Laws of Sines and Cosines and use them to
solve problems.
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the lateral area, surface area, and
volume of prisms, cylinders, cone, and pyramids in
mathematical and real-world settings.
D.2.f Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Identify and use
Pythagorean triples in right triangles to find lengths of the
unknown side.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
24. [G-SRT11] Understand and apply the Law of Sines and the Law of
Cosines to find unknown measurements in right and non-right
triangles (e.g., surveying problems, resultant forces).
Understand and apply theorems about circles.
25. [G-C1] Prove that all circles are similar.
26. [G-C2] Identify and describe relationships among inscribed angles,
radii, and chords. Include the relationship between central,
inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular
to the tangent where the radius intersects the circle. [G-C2]
27. [G-C3] Construct the inscribed and circumscribed circles of a triangle,
and prove properties of angles for a quadrilateral inscribed in a
circle.
28. [G-C4] Construct a tangent line from a point outside a given circle to
the circle.
D.3.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Circles; Identify and define lines
segments associated with circles (e.g., radii, diameters, chords,
secants, tangents)
D.3.b Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Circles; Determine the measure
of central and inscribed angles and their intercepted arcs.
D.3.c Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Circles; Find segment lengths,
angle measures, and intercepted arc measures formed by chords,
secants, and tangents intersecting inside and outside circles.
D.2.b Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Polygons; Identify medians,
altitudes, perpendicular bisectors, and angle bisectors of
triangles and use their properties to solve problems.
D.3.d Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Circles; Solve problems using
inscribed and circumscribed polygons.
D.3.c Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Circles; Find segment lengths,
angle measures, and intercepted arc measures formed by
chords, secants, and tangents intersecting inside and outside
circles.
Find arc lengths and areas of sectors of circles.
(Radian introduced only as unit of measure.)
29. [G-C5] Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define
the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
F.1.d Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Area and Perimeter; Find
arc lengths and circumferences of circles from given information
(e.g., radius, diameter, coordinates)
F.1.e Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Area and Perimeter; Find
the area of a circle and the area of a sector of a circle from
given information (e.g., radius, diameter, coordinates)
Translate between the geometric description and
the equation for a conic section.
30. [G-GPE1] Derive the equation of a circle of given center and radius
using the Pythagorean Theorem; complete the square to find
the center and radius of a circle given by an equation.
G.1.d Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Write equations for circles in standard
form and solve problems using equations and graphs
D.1.e Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Locate, describe, and draw a locus in a plane or space.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
Use coordinates to provide simple geometric
theorems algebraically. (Include distance
formula; relate to Pythagorean Theorem.)
31. [G-GPE4] Use coordinates to prove simple geometric theorems
algebraically.
G.1.b Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Apply the midpoint and distance
formulas to points and segments to find midpoints, distances,
and missing information
G.1.c Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use coordinate geometry to solve
problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
32. [G-GPE5] Prove the slope criteria for parallel and perpendicular lines
and use them to solve geometric problems (e.g., find the
equation of a line parallel or perpendicular to a given line that
passes through a given point).
C.1.d Using Logic and Proof to Reason Mathematically; Logic
and Proof; Use various methods to prove that two lines are
parallel or perpendicular (e.g., using coordinates, angle
measures)
D.1.f Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Apply properties and theorems of parallel and
perpendicular lines to solve problems.
G.1.a Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use slope to distinguish between and
write equations for parallel and perpendicular lines.
G.1.c Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use coordinate geometry to solve
problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
33. [G-GPE6] Find the point on a directed line segment between two
given points that partitions the segment in a given ratio.
G.1.c Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use coordinate geometry to solve
problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
34. [G-GPE7] Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles, e.g., using the distance
formula.*
F.2.a
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the lateral area, surface area, and
volume of prisms, cylinders, cone, and pyramids in
mathematical and real-world settings.
G.1.c Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use coordinate geometry to solve
problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
Use coordinates to provide simple geometric
theorems algebraically. (AL)
35. [AL] Determine areas and perimeters of regular polygons, including
inscribed or circumscribed polygons, given the coordinates of
vertices or other characteristics.
G.1.c Relating Geometric Ideas to the Coordinate Plane;
Coordinate Geometry; Use coordinate geometry to solve
problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
Explain volume formulas and use them to solve
problems.
36. [G-GMD1] Give an informal argument for the formulas for the
circumference of a circle, area of a circle, volume of a cylinder,
pyramid, and cone. Use dissection arguments, Cavalieri’s
principle, and informal limit arguments.
D.4.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Solids; Identify and classify
prisms, pyramids, cylinders, cones, and spheres and use their
properties to solve problems. F.2.a
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the lateral area, surface area, and
volume of prisms, cylinders, cone, and pyramids in
mathematical and real-world settings.
F.2.b
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Use cross sections of prisms, cylinders,
pyramids, and cones to solve volume problems.
E.1.f.
Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Apply relationships between
perimeters of similar figures, areas of similar figures, and
volumes of similar figures, in terms of scale factor, to solve
mathematical and real-world problems.
E.1.h. Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify and give properties of
congruent or similar solids.
37. [G-GMD3] Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.*
D.4.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Solids; Identify and classify
prisms, pyramids, cylinders, cones, and spheres and use their
properties to solve problems. F.2.a
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the lateral area, surface area, and
volume of prisms, cylinders, cone, and pyramids in
mathematical and real-world settings.
F.2.c
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the surface area and volume of a
sphere in mathematical and real-world settings.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
38. [AL] Determine the relationship between surface areas of similar
figures and volumes of similar figures.
QUALITYCORE COURSE STANDARD
D.4.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Solids; Identify and classify
prisms, pyramids, cylinders, cones, and spheres and use their
properties to solve problems. F.2.a
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the lateral area, surface area, and
volume of prisms, cylinders, cone, and pyramids in
mathematical and real-world settings.
F.2.c
Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems; Lateral Area, Surface
Area, and Volume; Find the surface area and volume of a
sphere in mathematical and real-world settings.
Visualize relationships between two-dimensional
and three-dimensional objects.
39. [G-GMD4] Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three-dimensional
objects generated by rotations of two-dimensional objects.
D.4.b Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Solids; Describe and draw
cross sections of prisms, cylinders, pyramids, and cones
Apply geometric concepts in modeling situations.
40. [G-MG1] Use geometric shapes, their measures, and their properties
to describe objects (e.g., modeling a tree trunk or a human
torso as a cylinder).*
41. [G-MG2] Apply concepts of density based on area and volume in
modeling situations (e.g., persons per square mile, British
Thermal Units (BTUs) per cubic foot)*
42. [G-MG3] Apply geometric methods to solve design problems (e.g.,
designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on
ratios).*
Understand independence and conditional
probability and use them to interpret data.
(Link to data from simulations or
experiments.)
43. [S-CP3] Understand the conditional probability of A given B as P(A
and B)/P(B), and interpret independence of A and B as saying
that the conditional probability of A given B is the same as the
probability of A, and the conditional probability of B given A is
the same as the probability of B.*
D.1.a Identifying, Classifying, and Applying the Properties of
Geometric Figures in Space; Points, Lines, Planes, and
Space; Identify and model plane figures, including collinear
and noncollinear points, lines, segments, rays, and angles
using appropriate mathematical symbols.
E.1.h. Comparing Congruent and Similar Geometric Figures;
Similarity and Congruence; Identify and give properties of
congruent or similar solids.
COMMENTS
Revised Janaury 2013 2010 ACOS GEOMETRY
QUALITYCORE COURSE STANDARD
44. [S-CP4] Construct and interpret two-way frequency tables of data
when two categories are associated with each object being
classified. Use the two-way table as a sample space to decide if
events are independent and to approximate conditional
probabilities. *
45. [S-CP5] Recognize and explain the concepts of conditional probability
and independence in everyday language and everyday
situations.*
Use the rules of probability to compute probabilities
of compound events in a uniform probability
model.
46. [S-CP6] Find the conditional probability of A given B as the fraction of
B’s outcomes that also belong to A, and interpret the answer in
terms of the model.*
47. [S-CP7] Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and
B), and interpret the answer in terms of the model.*
48. [S-CP8] Apply the general Multiplication Rule in a uniform probability
model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and
interpret the answer in terms of the model.*
Use probability to evaluate outcomes of decision.
(Introductory; apply counting rules.)
49. [S-CP9] Use permutations and combinations to compute probabilities
of compound events and solve problems.*
50. [S-MD6] Use probabilities to make fair decisions (e.g., drawing by
lots, using a random number generator).*
51. [S-MD7] Analyze decisions and strategies using probability concepts
(e.g, product testing, medical testing, pulling a hockey goalie at
the end of the game).
F.1.c. Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems1. Area and Perimeter; Use
area to solve problems involving geometric probability.
F.1.c. Using Length, Area, Perimeter, and Volume to Find
Quantities and Solve Problems1. Area and Perimeter; Use
area to solve problems involving geometric probability.
COMMENTS